Mrs May is said to be considering offering MPs further safeguards about the Irish backstop - the measure aimed at preventing a hard border on the island of Ireland which critics fear could leave the United Kingdom indefinitely bound into a customs union with the EU and prevent future trade deals with countries around the world.
However, she refused four times to rule out bringing her deal back to be voted on repeatedly if it is rejected by MPs.
That is broadly in line with other polls in recent months which show a deeply divided electorate, in which opinion has swung towards remaining in the EU. Britons in a 2016 referendum voted to leave the European Union, a political and economic partnership that now has 28 members, triggering months of tortuous negotiations that have left the country bitterly divided.
Asked how they would vote if another referendum were held to choose between May's deal or leaving without a deal, just 29% said they would pick May's agreement, compared to 64% who would opt for no deal. Removing those who are undecided, the split was 53 per cent in favour of another referendum and 47 per cent against.
MPs were due to vote on the deal in December, but with flagging support the Government pulled the vote in a bid to give more reassurances to doubters over the festive period.
British Prime Minister Theresa May's aides are believed to be planning to make parliament's approval of her Brexit deal conditional on Brussels providing further concessions, specifically on the thorny issue of the Irish backstop, the Telegraph reported on Sunday (Jan 6).
Also, the Northern Irish party that props up Ms.
Meanwhile, one group of cross-party lawmakers is working on a plan to derail any prospect of a no-deal Brexit, which appears to be the most likely option if May's gambit fails.
"If anyone should be anxious about the tariffs on beef and sheep then it should be the Irish because of course, we, the United Kingdom are net importers of food", Wilson said. In December, May made a decision to postpone a parliamentary vote meant to ratify the agreement at the last minute after it became clear that it would be overwhelmingly defeated in the House of Commons.
Officially slated for the week of January 14, the Commons vote is expected to be held on Tuesday, January 15.
"Practically, actually you couldn't get a referendum in time before the 29th of March - you'd be talking about extending Article 50", she said, referring to the two-year exit notice Britain sent to the European Union in March 2017.
May's advisers are understood to be considering an amendment making approval of the deal subject to the Government obtaining assurances that the Irish backstop, the fallback plan meant to prevent a hard border, will be temporary.
As part of her efforts to win support for her deal, May on Sunday reiterated that the agreement she negotiated was the only one that respects the 2016 referendum result, protects jobs and provides certainty to people and businesses.